\(\left|x-2\right|+7=2x\\ \Leftrightarrow\left|x-2\right|=2x-7\left(x\ge\dfrac{7}{2}\right)\\ \Leftrightarrow\left[{}\begin{matrix}x-2=2x-7\\x-2=7-2x\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=5\left(tm\right)\\x=3\left(ktm\right)\end{matrix}\right.\)
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